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Tensor Numerical Methods in Electronic Structure Calculations: Basic Algorithms and Applications de Venera Khoromskaia

Tensor Numerical Methods in Electronic Structure Calculations: Basic Algorithms and Applications

Autor Venera Khoromskaia, Boris Khoromskij
en Limba Engleză Hardback – 14 ian 2017
When applied to multidimensional problems, conventional numerical methods suffer from the so-called “curse of dimensionality,” which cannot be eliminated by parallel methods and high performance computers. In this book the authors explain basic tensor formats and algorithms, showing how Tucker tensor decompositions originating from chemometrics brought about a revolution when applied to problems of numerical analysis.
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Specificații

ISBN-13: 9783110370157
ISBN-10: 3110370158
Pagini: 250
Dimensiuni: 170 x 240 mm
Greutate: 0.68 kg
Editura: De Gruyter
Colecția De Gruyter
Locul publicării:Berlin/Boston

Notă biografică

Venera Khoromskaia and Boris N. Khoromskij, Max-Planck-Institute for Mathematics in the Sciences,Leipzig, Germany.

Descriere

Descriere de la o altă ediție sau format:
The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by parallel methods and high performance computers. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multidimensional functions and operators discretized on uniform Cartesian grids. We explain basic tensor formats and algorithms showing how the Tucker tensor decomposition originating from chemometrics made a revolution when applied to problems of the numerical analysis. On several examples from electronic structure calculations we show how the calculation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, enabling Matlab simulations using 3D grids of the size of 1015. This research monograph on a new field on numerical analysis written by the originators of tensor methods can be interesting for a wide audience of students and researchers from both numerical analysis and material science.
  • Novel numerical methods beating the supercomputing for multidimensional problems. They provide low-rank separable grid-based representation for arbitrary multivariate functions. Thus numerical integration of 3D convolution integrals is performed by 1D vector operations.
  • Novel 3D grid-based approach for the problems in electronic structure calculations. Enables calculation of 3D convolution integrals (with singularities) in1D complexity. Enables usage of grids of the order of 1014 in Matlab calculations on a laptop. General type grid-based basis functions can be used in Hartree-Fock calculations. Black-box type of calculations for arbitrary molecular geometries.
  • Efficient methods for periodic structures in the framework of the Hartree-Fock model.